带$N>3$牌的三人Kuhn扑克的平衡解：一种使用正则化和弧长延拓的新数值方法
Equilibrium solutions of three player Kuhn poker with $N>3$ cards: A new numerical method using regularization and arc-length continuation
摘要：
研究了三人Kuhn扑克的$N>3$牌均衡解。我们计算这些解决方案作为一个函数的初始锅的大小，$P$，使用一种新的方法的基础上正规化系统的多项式方程和不等式，定义的解决方案，并解决所产生的系统的非线性，代数方程组使用牛顿法和弧长延续的组合。我们发现，平衡解曲线的结构是非常复杂的，即使是对游戏与少量的卡。标准的三人库恩扑克，这是发挥与$N=4$卡，是从游戏有质的不同与$N>4$卡，因为简单的结构的价值投注和虚张声势的范围，每个球员。当$N>5$，我们发现有一种新型的均衡投注与中档卡，作为一个虚张声势对一个球员和价值投注对其他。
英文摘要：
We study the equilibrium solutions of three player Kuhn poker with $N>3$ cards. We compute these solutions as a function of the initial pot size, $P$, using a novel method based on regularizing the system of polynomial equations and inequalities that defines the solutions, and solving the resulting system of nonlinear, algebraic equations using a combination of Newton's method and arc-length continuation. We find that the structure of the equilibrium solution curve is very complex, even for games with a small number of cards. Standard three player Kuhn poker, which is played with $N=4$ cards, is qualitatively different from the game with $N>4$ cards because of the simplicity of the structure of the value betting and bluffing ranges of each player. When $N>5$, we find that there is a new type of equilibrium bet with midrange cards that acts as a bluff against one player and a value bet against the other.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
